Charge collection efficiency in photoconductive detectors under small to large signals

Hecht collection efficiency η0 and its formulations for exponential absorption have been widely used in modeling charge collection efficiency in photoconductive detectors. The basic assumption of the Hecht formulation is that the electric field in the device is uniform, i.e., the photoinjected carriers do not perturb the field. Here, we have used Monte Carlo simulations to model the initial injection of electron and hole pairs and their subsequent transport and trapping in the presence of an electric field, which is calculated from the Poisson equation. Each injected carrier is tracked as it moves in the semiconductor until it is either trapped or reaches the collection electrode. Trapped carriers do not contribute to the photocurrent but continue to contribute to the field through the Poisson equation. The instantaneous photocurrent iph(t) is calculated from the drift of the free carriers through the Shockley–Ramo theorem. iph(t) is integrated over the duration of the photocurrent to calculate the total collected charge and hence the collection efficiency ηr. ηr has been calculated as a function of the charge injection ratio r, the electron and hole ranges (drift mobility and lifetime products, μτ), mean photoinjection depth δ, and drift mobility ratio b. The deviation of the collection efficiency ηr from the uniform field case η0 can be as much as 30% smaller than the small signal model prediction. However, for a wide range of electron and hole schubwegs and photoinjection ratios, typical errors remained less than 10% at full injection, the worst case. The present study provides partial justification to the wide-spread use of the uniform-field collection efficiency η0 formula in various applications, even under high injection conditions.